The sculpture, by artist Paul Day, also marks the contribution made by civilians in the two conflicts between 1990 and 2014.
It is formed of two stone monoliths and a bronze medallion.
Its unveiling in Victoria Embankment Gardens on the bank of the River Thames followed a service for 2,500 war veterans and guests.
More than 800 UK military personnel and civilians died in three wars in the region.
The 1-million-pound monument was funded by a campaign by the Rupert Murdoch owned 'Sun on Sunday' newspaper.
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Mark Collins, a former RAF wing commander who did two tours of Afghanistan, said the memorial would be a focal point where people could reflect on the good that went on overseas as well as the sadness.
"It's important that we remember and reflect so we don't go down those roads again and we learn the lessons," he told the BBC.
The British monarch was joined by son and heir Prince Charles and his wife Camilla, grandsons, Prince William and Harry, and Duchess of Cambridge Kate Middleton.
British Prime Minister Theresa May and a number of former Prime Ministers, including David Cameron, John Major and Tony Blair, were among the thousands of guests.
The service was led by the Chaplain of the Fleet, the Venerable Ian Wheatley, who gave thanks to the civilians and military personnel who served in the Gulf region, Iraq and Afghanistan.
The first Gulf War saw 47 British troops killed from 1990-91. Another 454 died in Afghanistan from 2001-14, and 179 in Iraq from 2003-11.